Page History

Care must be taken when rearranging floating-point exceptions to ensure the greatest accuracy of the result.

According to C99, Section 5.1.2.3, "Program execution" \[[ISO/IEC 9899:1999|AA. C References#ISO/IEC 9899-1999]\]:

Rearrangement for floating-point expressions is often restricted because of limitations in precision as well as range. The implementation cannot generally apply the mathematical associative rules for addition or multiplication, nor the distributive rule, because of roundoff error, even in the absence of overflow and underflow. Likewise, implementations cannot generally replace decimal constants to rearrange expressions. In the following fragment, rearrangements suggested by mathematical rules for real numbers are often not valid.

Code Block
double x, y, z; /* ... */ x = (x * y) * z; /* not equivalent to x *= y * z; */ z = (x - y) + y ; /* not equivalent to z = x; */ z = x + x * y; /* not equivalent to z = x * (1.0 + y); */ y = x / 5.0; /* not equivalent to y = x * 0.2; */

...

Risk Assessment

Failing Failure to understand the limitations in precision of floating-point-represented numbers , and the implications of this on the arrangement of expressions, can cause unexpected arithmetic results.

...